Da Costa joined the Merrimack College Warriors of the NCAA's Hockey East conference in North Andover, Massachusetts, for the 2009–10 season.

[2][3] After receiving numerous offers from NHL teams to sign as a free agent, Da Costa opted to return to Merrimack for a second season in 2010–11.

Da Costa became just the sixth player born in France to play in the NHL, joining Cristobal Huet, Philippe Bozon, Pat Daley, Paul MacLean and André Peloffy, and the third French-born and -trained NHL player (along with Bozon and Huet and before Antoine Roussel, Pierre-Édouard Bellemare, and Yohann Auvitu).

[5][6] After an impressive training camp to start the 2011–12 season, Da Costa made the Senators' opening night roster and joined the team for their first game.

He registered his first NHL point on 8 October in his second game of the season, a goal in a 6–5 loss to the Maple Leafs against goaltender James Reimer.

[7] After scoring three goals and five points in 22 games in Ottawa, Da Costa was reassigned to their American Hockey League (AHL) affiliate, the Binghamton Senators, on 27 November 2011.

[10] On 12 July 2014, Da Costa left North America and signed as a free agent to a one-year contract with CSKA Moscow of the KHL.

[12] Returning to the KHL for the 2018–19 season with the Russian club, Avtomobilist Yekaterinburg, Da Costa posted 22 goals and 48 points in 58 games.

As a free agent after the season, Da Costa opted to continue in the KHL by signing a one-year deal with Lokomotiv Yaroslavl on May 1, 2019.

Da Costa returned for the 2009 World Junior Ice Hockey Championships - Division I held in Herisau, Switzerland, scoring four goals and 13 points in five games and helping France to a 3–2–0 tournament record.